How To Do A Rolling Sum Where The Width Depends On The Sum Itself? Top 3 Favorites

To perform a rolling sum where the width of the window depends on the sum itself, you can follow these steps:

1. Set an initial window size w and starting index i to 0.
2. Calculate the sum of the elements from index i to i + w.
3. If the sum is greater than or equal to a certain threshold value t, record it and increment the starting index i by 1. Otherwise, increment the window size w by 1 and repeat step 2.
4. Repeat steps 2 and 3 until the window size w exceeds the length of the input sequence.

Here is an example implementation in Python:

python
def rolling_sum(sequence, threshold):
    i = 0
    w = 1
    sums = []
    while w <= len(sequence):
        window_sum = sum(sequence[i:i+w])
        if window_sum >= threshold:
            sums.append(window_sum)
            i += 1
        else:
            w += 1
    return sums

You can call this function with a sequence of numbers and a threshold value to obtain a list of all rolling sums that exceed the threshold:

python
>>> sequence = [1, 2, 3, 4, 5, 6, 7, 8, 9]
>>> threshold = 12
>>> rolling_sum(sequence, threshold)
[15, 21, 27, 36]

In this example, the function finds all rolling sums that exceed the threshold of 12, where the width of each window is adjusted dynamically based on the sum itself.